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I didn't used to ever purchase AppleCare+ for my iPhones. I ended up changing my policy on it after my iPhone 5 sleep/wake button stopped working about one month after my 1 year warranty ended. To top it off, it happened exactly when our first child was born! Not the most stress-free time of life to have your phone break! I had to call apple support, and they agreed to override their replacement policy and replaced my phone anyway. For me, that ended up pushing me towards getting AppleCare+ on my phone.

Either way it's a risk, though different risks. I'm a very risk averse person. For me, my iPhone is one of a very small number of items I purchase extended warranties on. Usually, I think they're a waste of money.
 
To rigormortis,

I have never had to say any "password" of any style to get free support. Never. I am only asked which of my Apple kit I am calling about and we begin solving my problem.
 
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